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An Approach to the EOG Signal Segmentation Based

on Fuzzy Reasoning

AbstractIn this paper we presented an approach to segmenta-tion of an electrooculography (EOG) signal. For segmentation wehave used the elements of the fuzzy set theory. Results obtainedin our numerical experiments show usefulness of proposed

approach. Our method can be also used for the generating ofa learning set necessary for the neural networks or the fuzzyneural systems training.

Index TermsEOG signal, signal segmentation, fuzzy reason-ing, fuzzy clustering.

I. ITRODUCTION

The EOG signal is based on electrical measurement of the

potential difference between the cornea and the retina. The

cornea-retinal potential creates an electrical field in the front

of a head. This field changes in orientation as the eyeballs

rotate. The electrical changes can be detected by electrodes

which are placed near eyes. It is possible to obtain independentmeasurements from each of the one pair of eyes. For a healthy

man, the movement of eyes is coupled in the vertical direction.

Then it is adequate to measure the vertical motion of only

single eye together with the horizontal motion of a pair of

eyes. The amplitude of EOG signal varies from 50 to 3500

V with a frequency range of about DC-100 Hz. Its behavioris practically linear for gaze angles of30o [1]. It should bepointed out here that the variables measured in the human body

(any biopotentials) are almost always recorded with a noise

and often have a non-stationary features. Their magnitude

varies with time, even when all possible variables are under

control. This means that the variability of the EOG signals

depend on many factors that are difficult to determine [1].The EOG signal can be recorded in a horizontal and

vertical direction of eye movement. This requires nearly six

electrodes which are placed in the front of a human face. An

eyelid movement (blink) introduces a change in the potential

distribution around the eye [2] [3]. Another way to record an

eye movements signal and eye blinks is an application based

on the different reflection of the emitted infrared light from

eyelid and eyeball [5], [2].

Our aim is to detect these parts of the EOG signal, which

correspond to the saccadic eye movements. Saccadic parts of

the EOG signal distinguish on the signal as the small but rather

fast changes of amplitude. The saccade is the fastest movement

of an external part of the human body. The peak angular

speed of the eye during a saccade reaches up 1000 degrees

0 5 10 150

10

20

30

40

50

60

70

80

90

100

time [s]

Fig. 1. An example of the EOG signal. The amplitude of the signal has beennormalized.

per second. Saccades last from about 20 to 200 miliseconds[4]. In this paper we report the initial stage of our work which

concerns problem of bulding humanmachine interface.

The methods of signal segmentation require the number of

segments as an initial parameter [6], [7]. In our approach to the

segmentation problem, the number of segments is not required

as an initial parameter.

The paper is divided into the following sections: Section II

describes proposed segmentation method. Section III presents

obtained results from our numerical experiments. Finally, insetcion IV we draw some conclusions.

I I . SEGMENTATION THEE OG SIGNAL

The EOG signal represents an alectric activity of the eyeball

muscles. An example of the electrooculography signal has

been presented in figure 1. Looking at the example of the

EOG signal, it can be found the rapid changes of aplitude

correspond with consciously eye movement to another part of

the scene. Between rapid amplitude changes small and rather

fast changes of amplitude can be observed. These parts of the

analyzed signal are called saccadic eye motions. Let us define

the gradient of the EOG signal as

dx(n) = |x(n+ 1) x(n)| , (1)

{tprzybyla, tpander, rczabanski}@polsl.pl

HSI 2008 Krakow, Poland, May 25-27, 2008

1-4244-1543-8/08/$25.00 2008 IEEE

Division of Biomedical Electronics, Silesian University of Technology, Gliwice, Poland

Tomasz Przybya, Tomasz Pander, and Robert Czabanski

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0 500 1000 15000

0.5

1

1.5

2

2.5

Fig. 2. The gradient of EOG signal.

where x(n) is the n th sample of the EOG signal, 1 n N 1, and N is the lenght of the signal. Analyzing thegradient signal dx(n) the moment can be found, when largeaplitudes occur. It matches the change of observed object or

part of the scene. Hence, when the gradient values are small

then we deal with saccade movements. An example of the

EOG gradient signal has been presented in figure 2.

The notions large amplitude and small amplitude can be

interpreted from the fuzzy set theory point of view. So, we

can state that the interesting parts of analyzed signal occur

when the aplitudes of gradient signal are small.

Many fuzzy clustering methods can be utilized for the

estimation of the membership values. Namely, as clusteringresults we obtain the membership grades for the clustered

data, and the cluster prototypes. Unfortunately, after clustering

process only the membership grades for the samples from the

input data set are known. When the input data set would be

changed, for some samples from the data set we could not

estimate the membership values. In the worst case, only for

few samples from the input data set we could estimate the

membership values. So, in this paper, instead of clustering

data for each analyzed signal, theZ(x) membership functionhas been proposed in the following form:

Z(x) =

1 ifx < a,1 2

xa

ba

2ifa x a+b

2 ,

2

bx

ba

2if a+b

2 x b,

0 ifx > b

(2)

An example shape of the Z membersip function has beenpresented in figure 3.

The two parameters a and b can be computed in thefollowing way: for the clustered data set X and for the setsdefined as:

I1 = {i: 1 (xi)< , 1 i N}

I0 = {i: (xi)< , 1 i N} , (3)

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

x

m(x)

Fig. 3. Shape of the Zmembersip function, where a = 0.5 and b = 1.5

the parameter values ca be estimated from

a= 1

|I1|

iI1

xi,

b= 1

|I0|

iI0

xi,, (4)

The (xi) denotes the membership grade of the i-th samplefrom the data set, xi X and 1 i N, the parameter describes the tolerance limit explained further in this section.

The notations |I1| and |I0| correspond the cardinal numbersofI1 andI0 sets, respectively.

After the clustering process, the membership values are

equal to one, only for these samples from the input data setthat are equal to the cluster prototype (i.e. the distance between

the samples and the prototype is equal to zero) [8] [9]. Hence,

for the estimation of the a parameter value, the obtainedcluster prototype value corresponds to small cluster can be

applied. For the methods that utilize the kernel functions a

problem occurs for the cluster prototype value determination.

Therefore, to avoid such kind of problems, we have proposed

another way for estimation the a parameter value.

The proposed equations (3) and (4) can be interpreted as a

mean of these samples, that have the membersip grades not

smaller than(1 ) for the problem of the a parameter valueestimation. The membership grades are not higher than the

treshold during the b parameter value estimation.The segments (the saccade parts of the EOG signal) are

determined as these parts of the analyzed signal, for which the

membership values of thesmallfuzzy set of the gradient signal

exceed the treshold 0.5. Generally, when the membershipgrade values exceed1/c, where thec is the number of clusters.

After treshold procedure described above, the start point

and the end point of the obtained segments are different than

expected. So, as the final stage of the processing the EOG

signal, the nearest local extrema of the EOG signal have been

chosen to the obtained points.

Generally, the proposed approach could be described as

follows:

Normalize the EOG signal, increase the amplitude of the

signal by 100 times,

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0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fig. 4. The membership values for the small fuzzy set drawn by dots, andfor the large fuzzy set drawn by crosses

Compute the gradient signal,

Cluster the amplitudes of the gradient signal into two

groups: small amplitudes and large amplitudes,

For the small amplitudes fuzzy set compute the values of

theaand theb parameters of the Zmembership function, Chose these samples of the gradient signal which have

the membership grade to the small amplitudes fuzzy set

higher than 0.5, Finally, find the local extrema of the EOG signal and

chose these, that are nearest to the obtained points in the

previuos stage.

III. NUMERICAL EXPERIMENT

In this section, the example demonstrates the performance of

the proposed approach. In our investigations, the real, in vivo

acquired signal have been analyzed. As the data acquistion unit

we used the Biopack hardware. For the registration of eye

movements we have constructed a segment of LEDs placed

on sphere in 40 up to +40 degrees with 10 degrees step inhorizontal direction. The LEDs were displayed sequantially.

The proposed method has been applied to the raw signals. All

analyzed signals have not been preprocessed. The gradient

signal has been multiplied by 100 due to the roundoffproblems.

As first stage of the EOG signal segmentation, the gradientsignal based on (1) has been estimated. Next, the gradient

values have been clustered into two groups corresponding to

the small amplitude and the large amplitude fuzzy sets. As

the clustering method, we used the familiar fuzzy cmeans

clustering method (FCM) proposed by Bezdek. The following

parameters have been fixed for the clustering method:

the number of clusters c = 2, the fuzzyfier m = 2, the tolerance for the FCM method = 105.

The gradient clustering results have been sketched in figure 4.

After the clustering process, the a and the b parameter

values have been estimated. Value of the parameter hasbeen fixed to = 103. The comparison of the estimated

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fig. 5. The comparison between the Z membership drawn by crosses andobtained from clustering process drawn by dots

5.5 6 6.5 7 7.585

90

95

100

time [s]

Fig. 6. The obtained segments after the treshold process of the membershipgrades. Short part of the analyzed EOG has been presented due to the problemillustration. The segments are plotted as the horizontal lines, the beginningsand the ends of the segments are plotted by crosses.

(Z) membersip function and the obtained membership valuesfor the small data set, has been shown in figure 5.

Applying the tresholding of the membership grades of the

gradient signal, we obtain the segments these parts of the

EOG signal which correspond to the saccade movements. Due

to readility, only small part of the segmented signal has been

presented in figure 7. The segments obtained in the last stage

of proposed algorithm have been shown in figure 7.Finally, figure 8 presents the segmented EOG signal. The

saccade segments of the EOG signal have been plotted as

horizontal lines.

IV. CONCLUSIONS

In this work, a proposition of an approach to the segmen-

tation of an EOG signal has been introduced. The proposed

approach is based on the fuzzy logic. Our aim was to estimate

the position of the saccade parts. The proposed algorithm

deals with humanlike rules ie. the criterion can be described

by linguistic variables such as small, or large. It makes the

algorithm more general.

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5.5 6 6.5 7 7.585

90

95

100

time [s]

Fig. 7. The beginnigs and the ends of the segments after the last processingstage. The obtained local extrema are plotted as the crosses, and the segmentsare plotted as the horizontal lines.

0 5 10 150

10

20

30

40

50

60

70

80

90

100

time [s]

6.5 7 7.5 8 8.5 9 9.5 10 10.5 11

65

70

75

80

85

90

95

100

time [s]

Fig. 8. The segmented EOG signal. The whole signal (a) and the short partof the signal (b).

It should be mentioned, that no preprocessing has not been

applied. The recorded EOG signals were corrupted by noise,

and often the corruption signals have had the nonstationary

features.

In our future investigations we concern the preprocessing

stage. Specifically, the question of kinds of filters (if any) used

for improvement of the final results. Moreover, we touch on the

problem of estimation the signal slopes in the saccade parts,

and the problem of the influence of blinking should also be

considered.

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[2] Skotte J.H., Njgaard J.K., Jrgensen L.V., Christensen K.B., SjgaardG., Eye blinking frequency during different computer tasks quantifiedby electrooculography, Eur. J.Appl.Physiol., 2007, vol. 99, pp.113-119

[3] Lalonde M., Byrns D.,Gagnom L., Teasdale N., Laurendeau D., Realtime eye blink detection with GPUbased SIFT tracking, Fourth Cana-dian Conf. Computer and Robot Vision CRV 2007.

[4] Oster A., Lichtsteiner P., Delbrck, Liu SC., A SpikeBased SaccadicRecognition System, IEEE Symp. on Circuits and Systems 2007, pp.30833086.

[5] Caffier P.P., Erdmann U., Ullsperger P., Experimental evaluation of eye-blink parameters as a drowsiness measure, Eur. J. Appl. Physiol., 2003,vol. 89, pp.319-325,

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